Question

1. Suppose that labor and capital are perfect substitutes. The existing technology permits 1 machine to do the work of 2 workers. A firm wants to produce 100 units of output. Suppose the price of capital is $500 per machine per week. What combination of inputs will the firm use if the weekly salary of each worker is $300? What if the weekly salary is $225?

Answer 1

As the labour and capital are perfect subsitutes, the firm will be using only capital or only labour depending upon the relative price of the inputs. We are given the slope of the isoquant as 1/2. We can find the slope of the isocost which is given as w/r where w = wage rate, r = cost of capital. So the slope of isocost = 300/500 = 3/5. Since the slope of the isocost curve is steeper than the slope of the isoquant curve, the firm will hire only capital input.

When the salary becomes $225, the slope of the isocost curve becomes 225/500 = 0.45. Because the slope of the isocost curve is less than the slope of the isoquant curve, the firm in this case will hire only labour.